Question

Does this make any sense?

Answer 1

Answer:

B. 28

Step-by-step explanation:

If ΔABC ~ ΔDEC, then the corresponding sides are in proportion:

$\dfrac{AC}{DC}=\dfrac{AB}{DE}$

We have:

$AC=x\\DC=32-x\\AB=42\\DE=6$

Substitute:

$\dfrac{x}{32-x}=\dfrac{42}{6}$

$\dfrac{x}{32-x}=\dfrac{7}{1}$                cross multiply

$(1)(x)=(32-x)(7)$            use distributive property

$x=(32)(7)+(-x)(7)$

$x=224-7x$           add 7x to both sides

$8x=224$             divide both sides by 8

$x=28$